Such a shelter structure is described in patent FR 2 891 782. Such a structure presents the advantage of making it possible to load a container or a conventional cargo from above or from one of the sides of the deck. Nevertheless, until now, such a structure does not make it possible to optimize utilization of the height of the shelter structure. When the shelter structure is in the folded position, which position may be used during periods of road travel when the load deck is supporting a container, the spreaders project in part above the arches, since each spreader is connected to an arch by a pivot connection about an axis that is substantially parallel to the longitudinal axis of the cross-member of the arch. In the deployed position, the tops of the arches and the tops of the spreaders occupy substantially the same plane in order to form a roof that is substantially plane. The portions of the spreaders that project above the arches when the shelter structure is in its folded position constitute a loss of vertical loading volume for the shelter structure. It is necessary to lower the height of the arches in order to comply with road loading gauges while the structure is in its folded position.